Hyperspectral Image Unmixing Via Structural Sparse Representation

Spectral unmixing is an important problem in hyperspectral data exploitation. It amounts at characterizing the mixed spectral signatures collected by an imaging instrument in the form of a combination of pure spectral constituents(endmembers), weighted by their correspondent abundance fractions. Linear spectral unmixing is a popular technique in the literature which assumes linear interactions between the endmembers, thus simplifying the characterization of the mixtures and approaching the problem from a general perspective independent of the physical properties of the observed materials. However, linear spectral unmixing suffers from several shortcomings. First, it is unlikely to find completely pure spectral endmembers in the image data due to spatial resolution and mixture phenomena. Second, the linear mixture model does not naturally include spatial information, which is an important source of information(together with spectral information) to solve the unmixing problem.This thesis is mainly concerned with the algorithm of spectral unmixing which makes use of spectral libraries of materials collected on the ground or in a laboratory, thus circumventing the problems associated to image endmember extraction. Due to the increasing availability and dimensionality of spectral libraries, this problem calls for efficient sparse regularizers. The resulting approach is called sparse unmixing, which represents a unique contribution of this research work and which opens a new direction in the field of spectral unmixing, which is a very active research topic in the hyperspectral image analysis literature. The thesis major contributions are outlined as follows:1. Through the study of non-local similarity of spectral images, this thesis proposes a hyperspectral image unmixing algorithm combining the structural sparsity as priori knowledge. The core idea is to add structural sparsity to linear sparse unmixing model. Compared to the traditional 1-norm model, the structural sparsity is more stable and accurate. Structural sparse representation utilizes both the spectral and spatial redundancies of hyperspectral images and non-local similarity of spectral lines, leading to better reconstruction performance. Experiment results show that the approach performs better than other state-of-the-art method.2. Another contribution of this work is that a low-rank approach toward structural sparse coding to hyperspectral image unmixing is proposed. Low-rank approximating regularizer not only takes advantage of nonlocal similarity of spectral images but also improve the sparsity of abundance matrix. Experiment results show that the algorithm has validity and reliability and performs better than other state-of-the-art methods.